Journal of Integer Sequences, Vol. 10 (2007), Article 07.9.8

On a One-Parameter Family of Riordan Arrays and the Weight Distribution of MDS Codes

Paul Barry
School of Science
Waterford Institute of Technology

Patrick Fitzpatrick
Department of Mathematics
University College Cork


We use the formalism of the Riordan group to study a one-parameter family of lower-triangular matrices related to the weight distribution of maximum distance separable codes. We obtain factorization results for these matrices. We then derive alternative expressions for the weight distribution of MDS codes. We define related weight ratios and show that they satisfy a certain linear recurrence.

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(Concerned with sequences A007318 A113310 and A113311 .)

Received June 21 2007; revised version received November 16 2007. Published in Journal of Integer Sequences, November 20 2007.

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